Forcing Nets inside Forcing Nets

Programs which generate, solve, and analyze Sudoku puzzles

Forcing Nets inside Forcing Nets

Postby Hajime » Sun Mar 21, 2021 7:09 am

In this topic it is said that Forcing Nets inside Forcing Nets can solve the hardest puzzles.
creint wrote:My solver can now solve all the hardest puzzles.
Forcing nets inside forcing nets is the maximum that is required to solve them.

denis_berthier wrote:All the known puzzles can be solved with T&E at levels ≤=2.

2 questions:
    Is this heuristic experience or mathematical provable?
    Is it also applicable for Samurai or any other Gattai?
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Re: Forcing Nets inside Forcing Nets

Postby denis_berthier » Sun Mar 21, 2021 7:35 am

Hajime wrote:In this topic it is said that Forcing Nets inside Forcing Nets can solve the hardest puzzles.
creint wrote:My solver can now solve all the hardest puzzles.
Forcing nets inside forcing nets is the maximum that is required to solve them.

denis_berthier wrote:All the known puzzles can be solved with T&E at levels ≤=2.

2 questions:
    Is this heuristic experience or mathematical provable?
    Is it also applicable for Samurai or any other Gattai?

Forcing nets inside forcing nets is what Sudoku Explainer does and no puzzle is known that SE could not solve.

As for your question, how could a statement referring to "all the known puzzles" be mathematically proven?
All the puzzles in champagne's hardest list are in T&E(2). Moreover, they are in B7B or less, a much more constrained property, which leaves very little chance for finding any puzzle not in T&E(2). However, any amount of evidence doesn't make a mathematical proof.

This was about standard 9x9 Sudoku. It has been well known for a long time that larger Sudokus may require deeper levels of T&E.
As for Samurai or Gattai, I have no idea.
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